Can I Shunt the counterspell or boomerang ability of Cryptic Command? I know that if you Shunt a counterspell and change the target to Shunt, once it resolves, it fizzles as it no longer has a legal target. If the counterspell fizzles, will the second ability of Cryptic Command fizzle too, or will that resolve?

In order to play shunt targetting Cryptic Command, Cryptic Command must have 1 and only 1 target, which means you wont be able to do it if both of the first two modes are chosen. Remember also that the new target must be a legal target (though as you seem to know, you can change a counterspell's target to the misdirection spell that is still on the stack, only to have the misdirection spell leave the stack a moment later)

When any spell is about to resolve, it rechecks whether its targets are legal. If all of its targets are illegal, then the entire spell is countered, including the non-targetted portions.

So, for example, if your opponent plays Cryptic Command choosing the "counter target spell" mode and the "draw a card" mode, you respond with shunt, changing Cryptic Command's target to be Shunt. When Cryptic Command tries to resolve, it sees that its only target is illegal and the spell is countered and has no effect.